Capital Asset Pricing Model: Higher Expected Returns

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The Capital asset pricing model explains one of the most significant portfolio management theories; the CAPM model describes a linear relationship between the expected return and risk associated with an asset, preferably equities.

The CAPM model is very simple and easy to understand; yet very profound and widely accepted across financial industry.

What is CAPM?: The CAPM helps to ascertain the risk premium an investor should get before making any investment decision; especially before investing in a high risk security.

Let us try to understand with a very simple example. If we have $1 million with bank which gives us 4% interest rate without any kind of risk of default. Then by the end of the year my interest income would be $ 40,000.

Now if our portfolio manager suggests us to invest our money in the market like investing in an Index (Bank Nifty or S&P) or corporate bonds. Certainly, there is risk of default associated this investment and without probability of higher returns from risky investment, we would prefer to keep my money with bank.

So, until we are rewarded with higher return for investing in the market; we would not take the risk. This expected higher return is known as Market Risk Premium.

Let us define terminologies.

Rf  =  Risk Free return (Keeping with bank or investing in treasure bonds)

Rm = Return from the market (Investing in index)

Market Risk Premium = Rm – Rf

So, until market risk premium is not high enough; we would not invest in the market. Let us say our advisor promises 10% return in addition to 4% return from bank i.e. in total I would get 15% interest income which would be $ 150,000.

Let us add another term and that is investing in a particular security; e.g. investing in shares of reliance. Certainly risk of negative returns associated with Reliance is higher in comparison to investing in any index i.e. Reliance as a company might see losses for a given a quarter or a year but overall market would still be better placed. So again we would expect even higher return to invest in a single company rather than to invest in a given market. Accordingly, we expect even higher returns.

The Capital Asset Pricing Model explains; this higher expected return by investing in a given security.

Re = Expected return by investing in a given security

Then; Re = Rf + β*(Rm – Rf)

Where,

β*(Rm – Rf) is the security risk premium i.e. risk premium we expect in addition to risk free return while investing in a given security.

So, CAPM quantifies the expected return in addition to risk free return while we make any investment decision.

Assumptions of CAPM:

  • Risk Aversion: While investing in a high risk security; an investor will expect higher returns.
  • Utility Maximization: Every investor tries to maximize the return for a particular level of investment risk.
  • Friction less Market: There are no taxes, transaction costs or other hurdles while trading.
  • One Period Horizon: While assessing risk of investment for different securities; investor always asses risk for a particular period.
  • Homogenous Expectations: All investors behave or have same expectation like expectations of profit maximization.
  • Divisible assets: All the assets are infinitely divisible i.e. an investor can invest as small as he wants.
  • Competitive market: All the investors have equal influence in the market and no single investor could influence whole of the market i.e. all the investors have unbiased information in the market and could take informed decisions.

Revisit of CAPM Model:

Let us once again look into CAPM model and try to understand another important term which is the slope in CAPM linear equation.

Re = Rf + β*(Rm – Rf)

Beta (β): While assessing higher expected return we have to understand the higher risk (also known as Systematic Risk) associated with given security depends upon the correlation between the given security and the market.

Beta, measures how sensitive or responsive an asset’s returns are to the changes in the return of the market. Higher beta means return of a given security is highly correlated with returns of overall market.

A positive beta indicates; return of security moves in tandem with return of the market where as negative beta means return of a given security moves in opposite direction of the market.

E.G. Insurance is one such sector; while any kind of losses if insured would result into return from the insurance company otherwise we pay premium to insurance company.

Beta is calculated as: Ratio of Covariance between returns from the market and returns of a given security divided by variance of the market returns.

Beta (the systematic risk) for the market is always equal to 1; as Covariance of an asset with itself is equal to variance which would result into variance both into numerator and denominator on the above equation and hence results into 1.

Interpretation of Beta:

Case 1: Beta = 0; indicates no correlation with the chosen benchmark

Case2: Beta = 1; one indicates a stock has the same volatility as the market

Case3: Beta > 1; more than one indicates a stock that’s more volatile than its benchmark

Case4: Beta < 1; less than one is less volatile than the benchmark

Summary: According to the CAPM theory, the expected return of a particular security or a portfolio is equal to the rate on a risk-free security plus a risk premium. So, as per CAPM model any rational investor would invest in a given security, only if his risk taking ability will be rewarded with higher returns.

Required (or expected) Return = RF Rate + (Market Return – RF Rate)*Beta

 

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